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-1, 0, 1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,9
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REFERENCES
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C. K. Fan, Structure of a Hecke algebra quotient. J. Amer. Math. Soc. 10 (1997), no. 1, 139-167. [Page 156, f^1_n.]
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1).
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FORMULA
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From R. J. Mathar, Jul 26 2010: (Start)
a(n) = +a(n-1) +a(n-3).
a(n) = A078012(n-2), for n>=2.
G.f.: ( 1-x^2-x ) / ( -1+x+x^3 ). (End)
From Michael Somos_, Jan 08 2014: (Start)
a(n) = A077961(2-n) for all n in Z.
a(n)^2 - a(n-1)*a(n+1) = A077961(n-5). (End)
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EXAMPLE
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G.f. = -1 + x^2 + x^5 + x^6 + x^7 + 2*x^8 + 3*x^9 + 4*x^10 + 6*x^11 + ...
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MATHEMATICA
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LinearRecurrence[{1, 0, 1}, {-1, 0, 1}, 50] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)
a[ n_] := If[ n < 3, SeriesCoefficient[ 1 / (1 + x^2 - x^3), {x, 0, 2 - n}], SeriesCoefficient[ x^5 / (1 - x - x^3), {x, 0, n}]]; (* Michael Somos, Jan 08 2014 *)
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PROG
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(Haskell)
a135851 n = a135851_list !! n
a135851_list = -1 : 0 : 1 : zipWith (+) a135851_list (drop 2 a135851_list)
-- Reinhard Zumkeller, Mar 23 2012
(PARI) {a(n) = if( n<3, polcoeff( 1 / (1 + x^2 - x^3) + x * O(x^(2-n)), 2-n), polcoeff( x^5 / (1 - x - x^3) + x * O(x^n), n))}; /* Michael Somos, Jan 08 2014 */
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CROSSREFS
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Cf. A013979, A077961, A078012, A107458.
Sequence in context: A068921 A000930 A078012 * A199804 A101913 A352042
Adjacent sequences: A135848 A135849 A135850 * A135852 A135853 A135854
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane, Mar 08 2008
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STATUS
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approved
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